几类图的负对控制数

On minus paired-domination number of some graphs

设D V是图G=(V,E)的任意一个对控制集,如果一个函数f:V→{-1,0,1}满足条件1)对任意点v∈D,有f(v)=1,对任意点v∈V-D,有f(v)≤0,2)对任意点v∈V,均有f(N[v])≥1,则称函数f为图G的负对控制函数。负对控制函数f的重量f(V)是V中所有点的函数值之和,图G的负对控制数γp-(G)=min{f(V)|f是图G的负对控制函数}。本文研究一些图的负对控制数。

Let D lohtain in V be any paired-dominating set of G=（V, E）. A minus paired-dominating function of G is a function of the form f：V→{-1,0,1} such that f（v）=1 for any vertex ν∈D,f（v）≤0 for any vertex ν∈V-D,and f（N[ν]）≥1 for any vertex ν ∈ V. The weight of a minus paired-dominating function f is the sum of f（ν）, over all vertices v E V. The minus paired-domlnation number of a graph G, γp-（G）= min{ f（V） ｜f is a minus paired-dominating function of G}. In this paper, we discuss the minus paired-domlnation number of some graphs.